Any object can emit and absorb radiation and the power of emission can be represented by the Stefan-Boltzmann law:

$$P=A\epsilon\sigma T^4$$

In many texts the net power radiated is the difference between the power emitted and the power absorbed:

$$P_{net}=A\epsilon\sigma (T^4-T_s^4)$$

where T_s is the temperature of the surroundings.

Why can the surrounding and the object share the same $\epsilon$ ?

If we try to find out the radiation emitted from the surrounding it should be $P_s=A\epsilon_s\sigma T_s^4$, and if $\epsilon_s<\epsilon$, we will get a strange result that energy radiated from the surrounding is less than the radiation absorbed by the body from the surrounding. What am I missing?